Abstract: Curved spaces, such as surfaces, provide a rich setting for the study of partial differential equations (PDEs). Building upon the extensive research conducted on PDEs in flat spaces, the ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

Researchers have made a breakthrough in the ability to solve engineering problems. In a new paper published in Nature entitled, “A scalable framework for learning the geometry-dependent solution ...

Abstract: Closed-form solutions, including arbitrary functions, of the system of nonlinear partial differential equations in plane rigid perfect plasticity are extracted. This system is reduced to a ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can ...

1 Department of Mathematics, University of Education, Okara Campus, Okara, Pakistan. 2 Center for Undergraduate Studies, University of the Punjab, Lahore, Pakistan. 3 Air University Multan Campus, ...